An Oscillating Holographic Dark Energy in $f(R)$ Gravity

TL;DR

This paper explores an oscillating holographic dark energy model within $f(R)$ gravity in a Bianchi-II universe, revealing oscillatory behavior of the equation of state and violations of energy conditions near bounce points.

Contribution

It provides exact solutions for LRS Bianchi-II cosmology with holographic dark energy in $f(R)$ gravity, highlighting oscillating EoS and energy condition violations.

Findings

EoS parameter oscillates between -0.778 and 1.016.

Null Energy Condition is violated near bouncing points.

The model exhibits physically and geometrically consistent behavior.

Abstract

In this article, we investigated a Locally Rotationally Symmetric (LRS) Bianchi-II cosmological model with matter and Holographic Dark Energy (HDE) in the context of $f(R)$ theory of gravity. In order to find exact solutions to the field equations, we assumed that the Shear scalar $(\sigma)$ is proportional to Expansion scalar $(\theta)$. For HDE, it is observed that the Equation of state (EoS) parameter $ \omega_{\Lambda} $ has an oscillating nature and lies in $[-0.778,\, 1.016].$ Also, we have studied the validity of energy conditions and shows that Null Energy Condition (NEC) is violated near the bouncing points. Moreover, we analysed the physical and geometrical aspects of the investigated model. Keywords: Holographic dark energy, LRS Bianchi-II, $f(R)$ gravity.